You'll do this as a combination of open and shorted winding measurements.
As a first step, sketch a transformer equivalent circuit to clarify your definition of Lm, Ls and transformer ratio. Different models are used in literature, the difference matters particularly for large Ls related to Lm.
If you have the circuit, you should be able to calculate easily which inductance values will be seen at the primary respectively secondary terminals with the other winding open or shorted.
You select capacitors for a resonance frequency around the intended operation frequency, connect the transformer in a (preferably series) resonance circuit to a generator and tune for resonance (maxim voltage across L and C). Repeat for all inductance values you want to measure.